Aman can row 40 km upstream and 60 km downstream in 13 hours. He can also tow 50 km pamat
In the given context, what is the rate of the current?
Options
2.5 km/hr
3.5 km/hr
4.5 km/hr
5.5 km/hr
Cannot be determined
Answers
Correct Question :- A man can row 40km upstream and 55km downstream in 13 hours . also he can row 30km upstream and 44km downstream in 10 hours. what is the rate of the current ?
Solution :-
Let us assume that, speed of man in still water is x km/h and speed of current is y km/h .
so,
→ In upstream man speed = (x - y) km/h .
→ In downstream man speed = (x + y) km/h .
we know that,
- Time = Distance / speed .
so,
→ 40/(x - y) + 55/(x + y) = 13
→ 30/(x - y) + 44/(x + y) = 10
now, let us assume that,
- 1/(x - y) = u
- 1/(x + y) = v
then,
→ 40u + 55 v = 13 -------- Eqn.(1)
→ 30u + 44 v = 10 -------- Eqn.(2)
Multiply Eqn.(1) by 3 and Eqn.(2) by 4 and subtracting result of Eqn.(1) from Eqn.(2) we get,
→ 4(30u + 44v) - 3(40u + 55v) = 4*10 - 3*13
→ 120u - 120u + 176v - 165v = 40 - 39
→ 11v = 1
→ v = (1/11)
putting value of v in Eqn.(1)
→ 40u + 55*(1/11) = 13
→ 40u + 5 = 13
→ 40u = 13 - 5
→ 40u = 8
→ u = (8/40)
→ u = (1/5)
therefore,
→ 1/(x - y) = u
→ 1/(x - y) = 1/5
→ x - y = 5
and,
→ 1/(x + y) = v
→ 1/(x + y) = 1/11
→ x + y = 11
adding both,
→ x - y + x + y = 5 + 11
→ 2x = 16
→ x = 8 km/h .
hence,
→ 8 + y = 11
→ y = 11 - 8
→ y = 3 km/h (Ans.)
Hence, Rate of current is 3 km/h.
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